The number of fifty-cent coins in a basket was 300% more than the number of ten-cent coins. 10 fifty-cent coins were taken out and exchanged for ten-cent coins. The number of 50-cent coins became
211 less than the number of 10-cent coins. How much money is there in the basket?
| |
Fifty-cent
(1) |
Ten-cent
(2) |
Make u the same
(2)x4 = (3) |
| Before |
4 u |
1 u |
4 u |
| Change |
- 10 |
+ 50 |
+ 200 |
| After |
9 p |
11 p |
44 p |
100 + 300100=
400100 =
41 At first
Fifty-cent coins : Ten-cent coins
4 : 1
1 -
211 =
911 In the end
Fifty-cent coins : Ten-cent coins
9 : 11
Total value of 50-cent coins to be taken out
= 10 x 50
= 500¢
Total number of 10-cent coins to be exchanged for
= 500 ÷ 10
= 50
Notice that the number of 10-cent coins is 1 u at first. So, instead of making p the same, we can make u the same so we create one extra equation instead of 2.
4 u - 10 = 9 p
4 u = 9 p + 10 --- (1)
1 u + 50 = 11 p --- (2)
(2)x4
4 u + 200 = 44 p
4 u = 44 p - 200 --- (3)
(3) = (1)
44 p - 200 = 9 p + 10
44 p - 9 p = 10 + 200
35 p = 210
1 p = 210 ÷ 35 = 6
The total value of the coins at first and in the end remains unchanged.
Total value of fifty-cent coins in the end
= 9 p x 50
= 9 x 6 x 50
= 2700¢
Total value of ten-cent coins in the end
= 11 p x 10
= 11 x 6 x 10
= 660¢
Total value of the coins
= 2700 + 660
= 3360¢
= $33.60
Answer(s): $33.60
